PSI - Issue 5

Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1299–1303 Jesús Toribio et al./ Structural Integrity Procedia 00 (2017) 000 – 000

1301 3

w

t

a

r

b

(a)

w

2t

2a

r

b

(b)

Fig. 1. Section of the plate containing: (a) corner crack; (b) surface crack.

p

a

p

a





b

b

(a)

(b)

Fig. 2. Angle  defining a point p at the crack front: (a) a / b ≤ 1; (b) a / b > 1.

The basic hypothesis of the modelling procedure consists of considering that the crack front advances by fatigue following the Paris law proposed by Paris and Erdogan (1963),

a C K N  

d

m

(2)

d

always maintaining the elliptical shape. The crack front is discretized as a set of points. Later, each point i is advanced in direction perpendicular to such a front. The crack increment at the point of maximum SIF, F {max}, is the maximum one Δ a {max} (constant), while in the remaining points the crack advance Δ a ( i ) is calculated through the following equation:

m

  

   

F i

( )

    max 

( )    a i

a

(3)

F

max

Finally, the advanced crack front is obtained by fitting a new ellipse to the calculated set of points by the least square method. The process is iteratively repeated up to obtaining the required crack depth. A convergence study was performed to determine the most adequate parameters for the computations.